<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div class=""><div class="">(重複で受け取られた方はご容赦ください)</div>皆様，<br class=""><br class="">秋田大の新屋です．</div><div class=""><br class=""></div><div class="">2月28日〜3月1日の東工大でのJacques Sakarovitch先生の連続講演会について，開催時間が変更されましたので，</div><div class="">概要を改めて再通知させていただきます．</div><div class=""><br class=""></div><div class="">同日に東工大にて行われるプログラミング研究会と時間が重なっていたため，開始時刻を遅らせて</div><div class="">Lecture/Seminar ともに16:30からの開始とさせていただきました．＊会場は変更ありません．</div><div class=""><br class=""></div><div class=""><br class=""></div><div class="">========== Lecture ========== </div><div class=""><div class=""><div class=""><div class="">Time:</div><div class="">16:30 ~ 17:30, February 28, 2018 (Wed.)</div><div class=""><br class=""></div><div class=""><br class=""></div><div class="">Venue:</div><div class="">Room W935, West Bldg. 9, Tokyo Institute of Technology (Ookayama Campus)</div><div class=""> 東京工業大学大岡山キャンパス 西9号館 W935講義室 (西9号館東側(芝生スロープ側)入口を入って階段を1階上がって左側)</div><div class=""><br class=""></div><div class=""><br class=""></div><div class="">Title:</div><div class="">Automata and expressions</div><div class=""><br class=""></div><div class="">Jacques Sakarovitch </div><div class="">CNRS / Paris Diderot University and Telecom ParisTech</div><div class=""><br class=""></div><div class=""><br class="">Abstract:<br class="">Not many results in Computer Science are recognised to be as basic and<br class="">fundamental as Kleene Theorem. It states the equality of two sets of<br class="">objects that we now call languages.<br class=""><br class="">In this lecture, I propose a slight change of focus on this result and show </div><div class="">how it is mainly the combination of two families of algorithms: </div><div class="">algorithms that transform an automaton into an expression on one hand </div><div class="">and algorithms that build an automaton from an expression on the other.</div><div class=""><br class="">The first purpose is to compare the results of these algorithms, </div><div class="">in order to understand they are indeed not so different. </div><div class="">And also to devise means to keep these results as small as possible.<br class=""><br class="">The second benefit of isolating this part of Kleene Theorem is to allow<br class="">its extension much beyond languages: to subsets of arbitrary monoids<br class="">first, and then, with some precaution, to subsets with multiplicity, </div><div class="">that is, to formal power series.</div><div class="">===========================</div></div><div class=""><br class=""></div><div class=""><br class=""></div></div><div class=""><div class=""><div class=""><div class=""><div class="">========== Seminar ========== </div><div class="">Time:</div><div class=""><div class=""><div class="">16:30 ~ 17:30, March 1, 2018 (Thu.)</div><div class=""><br class=""></div></div></div><div class=""><br class=""></div><div class="">Venue:</div><div class=""><div class="">Multi-Purpose Digital Hall, West Bldg. 9, Tokyo Institute of Technology (Ookayama Campus)</div><div class=""> 東京工業大学大岡山キャンパス 西9号館 ディジタル多目的ホール (西9号館東側(芝生スロープ側)入口を入ってすぐ)</div></div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""><div class="">Title:</div></div><div class="">Conjugacy and equivalence of weighted automata</div><div class=""><br class=""></div><div class=""><div class="">Jacques Sakarovitch </div><div class="">CNRS / Paris Diderot University and Telecom ParisTech</div><div class=""><br class=""></div><br class="">Abstract:<br class="">As a main thread of this talk, I present the proof of the following result:<br class=""><br class="">If two regular languages $L$ and $K$ have the same generating<br class="">functions, that is, for every integer $n$ they have the same number of<br class="">words of length $n$, there exists a rational bijection realised by a<br class="">letter-to-letter transducer that maps $L$ onto $K$.<br class=""><br class="">This statement is a consequence of a refinement of the decidability of<br class="">the equivalence of two automata with multiplicity in $N$. It gives us<br class="">the opportunity to review first the basic definitions and results on<br class="">weighted finite automata, and second to revisit the `classical' theory<br class="">of reduction of automata with two notions borrowed to symbolic<br class="">dynamics: conjugacy and the Finite Equivalence Theorem.</div><div class="">===========================<br class=""><br class=""></div><div class=""><br class=""></div><div class="">大岡山キャンパスまでの行き方は以下をご覧ください：<br class=""><a href="https://www.titech.ac.jp/maps/" class="">https://www.titech.ac.jp/maps/</a> <br class="">西9号館までの行き方は<br class=""><a href="http://www.dst.titech.ac.jp/outline/facility/hall.html" class="">http://www.dst.titech.ac.jp/outline/facility/hall.html</a><br class="">の中の地図をご覧ください。</div><div class=""><br class=""></div></div></div></div></div><div class=""><div class="">以上，どうぞよろしくお願いします．</div></div><div class=""><br class=""></div><div class="">秋田大学 数理科学コース 新屋良磨 <a href="mailto:ryoma@math.akita-u.ac.jp" class="">ryoma@math.akita-u.ac.jp</a></div><div class=""><div class="">(共催：東京工業大学 情報理工学院 鹿島亮)</div></div></div><div><br class=""><blockquote type="cite" class=""><div class="">On Feb 1, 2018, at 15:09, Ryoma Sin'ya <<a href="mailto:ryoma@math.akita-u.ac.jp" class="">ryoma@math.akita-u.ac.jp</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><meta http-equiv="Content-Type" content="text/html; charset=utf-8" class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div class="" style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;"><div class=""><div class="">(重複で受け取られた方はご容赦ください)</div>皆様，<br class=""><br class="">秋田大の新屋です．</div><div class=""><br class=""></div><div class="">下記の要領にて，フランスからJacques Sakarovitch先生を東工大にお招きしSeminar および Lecture を実施いたします．</div><div class="">＊SeminarとLectureで日時・会場が異なりますのでご注意ください．</div><div class=""><div class=""><br class=""></div><div class="">Sakarovitch先生は現代のオートマトン理論を牽引する世界的研究者であり，この連続講演会は</div><div class="">計算機科学に携わる多くの方に興味を持っていただけると思います．</div></div><div class="">参加申し込みなどは不要ですので，どうぞふるってご参加ください．</div><div class=""><br class=""></div><div class=""><div class=""><div class=""><br class=""></div><div class="">なお，2月28日(水)のLectureでは，古典的なKleeneの定理(正規表現とオートマトンの表現力の等価性)の</div><div class="">精密化・一般化に関する講義をしてもらいます．</div><div class="">本講義では現代的なオートマトン理論の基礎を説明してもらう予定ですので，学生の皆様もどうぞふるってご参加ください．<br class=""></div></div><div class=""><br class=""></div><div class=""><div class="">また，3月1日(木)のSeminarでは，Sakarovitch先生自身のこれまでの研究成果を中心に講演してもらう予定です．</div><div class="">下記のSeminar概要にて述べられている主結果については，拙著サーベイ論文「オートマトン理論再考」</div><div class=""><span class="Apple-tab-span" style="white-space: pre;"> </span><a href="https://www.jstage.jst.go.jp/article/jssst/34/3/34_3_3/_article/-char/ja/" class="">https://www.jstage.jst.go.jp/article/jssst/34/3/34_3_3/_article/-char/ja/</a></div><div class="">の4.4節でほんの少しだけ解説されていますので，興味のある方はどうぞこちらもご参照ください．</div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""><div class=""><div class="">========== Lecture ========== </div></div><div class="">Time:</div><div class="">15:20 ~ 16:20, February 28, 2018 (Wed.)</div><div class=""><br class=""></div><div class=""><br class=""></div><div class="">Venue:</div><div class="">Room W935, West Bldg. 9, Tokyo Institute of Technology (Ookayama Campus)</div><div class=""> 東京工業大学大岡山キャンパス 西9号館 W935講義室 (西9号館東側(芝生スロープ側)入口を入って階段を1階上がって左側)</div><div class=""><br class=""></div><div class=""><br class=""></div><div class="">Title:</div><div class="">Automata and expressions</div><div class=""><br class=""></div><div class="">Jacques Sakarovitch </div><div class="">CNRS / Paris Diderot University and Telecom ParisTech</div><div class=""><br class=""></div><div class=""><br class="">Abstract:<br class="">Not many results in Computer Science are recognised to be as basic and<br class="">fundamental as Kleene Theorem. It states the equality of two sets of<br class="">objects that we now call languages.<br class=""><br class="">In this lecture, I propose a slight change of focus on this result and show </div><div class="">how it is mainly the combination of two families of algorithms: </div><div class="">algorithms that transform an automaton into an expression on one hand </div><div class="">and algorithms that build an automaton from an expression on the other.</div><div class=""><br class="">The first purpose is to compare the results of these algorithms, </div><div class="">in order to understand they are indeed not so different. </div><div class="">And also to devise means to keep these results as small as possible.<br class=""><br class="">The second benefit of isolating this part of Kleene Theorem is to allow<br class="">its extension much beyond languages: to subsets of arbitrary monoids<br class="">first, and then, with some precaution, to subsets with multiplicity, </div><div class="">that is, to formal power series.</div><div class="">===========================</div></div><div class=""><br class=""></div><div class=""><br class=""></div></div><div class=""><div class=""><div class=""><div class=""><div class="">========== Seminar ========== </div><div class="">Time:</div><div class=""><div class=""><div class="">15:20 ~ 16:20, March 1, 2018 (Thu.)</div><div class=""><br class=""></div></div></div><div class=""><br class=""></div><div class="">Venue:</div><div class=""><div class="">Multi-Purpose Digital Hall, West Bldg. 9, Tokyo Institute of Technology (Ookayama Campus)</div><div class=""> 東京工業大学大岡山キャンパス 西9号館 ディジタル多目的ホール (西9号館東側(芝生スロープ側)入口を入ってすぐ)</div></div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""><div class="">Title:</div></div><div class="">Conjugacy and equivalence of weighted automata</div><div class=""><br class=""></div><div class=""><div class="">Jacques Sakarovitch </div><div class="">CNRS / Paris Diderot University and Telecom ParisTech</div><div class=""><br class=""></div><br class="">Abstract:<br class="">As a main thread of this talk, I present the proof of the following result:<br class=""><br class="">If two regular languages $L$ and $K$ have the same generating<br class="">functions, that is, for every integer $n$ they have the same number of<br class="">words of length $n$, there exists a rational bijection realised by a<br class="">letter-to-letter transducer that maps $L$ onto $K$.<br class=""><br class="">This statement is a consequence of a refinement of the decidability of<br class="">the equivalence of two automata with multiplicity in $N$. It gives us<br class="">the opportunity to review first the basic definitions and results on<br class="">weighted finite automata, and second to revisit the `classical' theory<br class="">of reduction of automata with two notions borrowed to symbolic<br class="">dynamics: conjugacy and the Finite Equivalence Theorem.</div><div class="">===========================<br class=""><br class=""></div><div class=""><br class=""></div><div class="">大岡山キャンパスまでの行き方は以下をご覧ください：<br class=""><a href="https://www.titech.ac.jp/maps/" class="">https://www.titech.ac.jp/maps/</a> <br class="">西9号館までの行き方は<br class=""><a href="http://www.dst.titech.ac.jp/outline/facility/hall.html" class="">http://www.dst.titech.ac.jp/outline/facility/hall.html</a><br class="">の中の地図をご覧ください。</div><div class=""><br class=""></div></div></div></div></div><div class=""><div class="">以上，どうぞよろしくお願いします．</div></div><div class=""><br class=""></div><div class="">秋田大学 数理科学コース 新屋良磨 <a href="mailto:ryoma@math.akita-u.ac.jp" class="">ryoma@math.akita-u.ac.jp</a></div><div class=""><div class="">(共催：東京工業大学 情報理工学院 鹿島亮)</div></div></div></div>
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